Customer Reviews: An Introduction To Quantum Field Theory (Frontiers in Physics)
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on December 15, 2001
This is a difficult book to review. That a detailed study of several textbooks is needed for a thorough introduction to QFT is a well-known maxim among students of the subject. Every QFT text excels in some areas and struggles in others, and Peskin and Schroeder's book (P&S) is no exception. P&S chooses to emphasize performing calculations in the Standard Model (SM), and the chapters pertaining to this topic are excellent. Chapters 5 and 6, covering tree and one-loop calculations in QED, are invaluable, as are chapters 20 and 21, which detail the electroweak theory.
Several of the formal aspects of QFT are shunted in P&S, as must something be neglected in every QFT text that is stable against gravitational collapse. The general representation theory of the Lorentz group is the most glaring omission in P&S. Chapter 1 of Ramond's "Field Theory: A Modern Primer" treats this topic quite well. The LSZ reduction formulae are derived and discussed more clearly in Pokorski's "Gauge Field Theories", as are BRST symmetry and free field theory. For those interested in undertaking detailed phenomenological studies of the SM or some extension thereof, Vernon Barger's "Collider Physics" is also recommended.
Despite its shortcomings, P&S remains the best QFT reference currently available. It's the book I turn to first when confronted in research papers with field theoretic puzzle that I just can't crack. If you buy only one QFT text, buy P&S.
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on March 25, 1998
I worked through the most of this book in explicit detail (the only way to get the full benefit, in my humble opinion), and, while it was very good at teaching the methods for deriving and computing Feynman diagrams, it often sacrifices pedagogy for explicit calculation. For instance, while there is a brief discussion of representations of the Lorentz group, the book gives no indication of how to construct and work with fields of higher spin. Also, I found their discussion of the LSZ reduction formulae rather impenetrable. (Their discussion of BRST symmetry, in contrast, is very readable and easily understood.) So, while I would recommend this book to anyone who wants to learn to do calculations in quantum field theory, it is imperative that they supplement this book with other sources that treat important topics, like the CPT theorem, general representation theory, and non-perturbative phenomena (which are barely mentioned here), in detail. (Also, there are a rather large number of unfortunate typos in the first edition...)
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on May 27, 2006
The main problem of this book: what exactly is it supposed to be?

If it is an introduction, then the opening chapters are written at a level too sophisticated that an average first-time student can't handle.

If it aims to be a "bible" of the subject, then the later chapters are far too technical, loaded with only Feynman diagram calculations for standard model. Not being a phenomenologist, I personally have very little interest in all the technical detail, and apparently several other reviewers share my view here.

Now let me gives some examples to support my claim.

First, C, P and T symmetries are introduced very early on (right after Dirac spinor), and in a very formal way. Yes, they logically belong there, but in an "introduction" of the subject you don't throw out an isolated topic like this which you don't make use of in the following few hundred pages.

The part on cannonical quantization is written at a very fast pace. A complex scalar field is probably the first model you can construct with charged particles. And guess what kind of treatment it receives in this book? Not a single word in the main text. The problem 2 of that chapter essentially asks you to work out the content of this model with few hints given. If you have troble working it out, which is not uncommon for a first-timer, then you won't see the logic behind the decomposition of a complex Dirac field either. This is done in the following chapter, with no explaination.

Like the charged scalar field example, some important pieces of knowledge are hidden only in the exercises. So if you treat these high-power opening chapters as your bible-type reference, you will often end up in the frustrating situation that the book tells you to work out by yourself what you are seeking in the first place.

Now get to the later parts of the book. As I mentioned above, the second half of the book is almost conceptually too simple, overloaded with technical details.

This downfall begins around the renormalization group. On the back of this book, this Prof. Micheal Dine is qouted: "it is the only field theory text with a thoroughly modern, Wilsonian treatment of renormalization". The connection between the Wilsonian idea and dimensional regularization/renormalization scale is shaky at best. You read the text, and are left puzzled at the magic: how does a cut-off scale become some (much lower) arbitrary momentum scale? No explaination. The Wilsonian theory is completely isolated and have little connection with the rest of the renormalization section.

Furthermore, the book does not do a very good job on Lie algebra and non-abilien Lie groups. I mean, come on, if this is an "introduction" type of book, make it more readable. If this is a "bible" type of book, make it more comprehensive.

Having voiced all my bad opinions, I have to admit that the book has its merit. Bottom line is, this is a book written by phenomenologists for phenomenologists. If you view it from such an angle, it is not too badly written after all, and does cover most of the important topics a phnomenologist would want to know. But you may want to start from a more accessible text such as Ryder.

If you are a theorist, but not a phenomenologist, then, well, let's say the ability of getting through the first part perfectly is the minimum requirement for your research.

If you are an experimentalist, don't bother.
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The authors give an excellent overview of the physical concepts and computational aspects of quantum field theory. They stress the situation behind the subject, and endeavor to remain as concrete as possible. Abstract mathematical constructions are left to more advanced texts in quantum field theory. The authors characterize their book as an updating of the two volume set of Bjorken and Drell.
The main emphasis of the book is on quantum electrodynamics (QED), the most successful of quantum field theories. The representation and analysis of the physical processes of QED is done via Feynman diagrams, with electron-positron annihilation leading off the discussion. Recognizing that the exact expression for the amplitude of this process is not known, perturbation theory is used to give an approximate representation for it via an infinite series with each term involving successively higher powers of the strength of the coupling between the electrons and photons (i.e. the charge). Each term is represented as a Feynman diagram. This is followed by a discussion of the quantum field theory of the Klein-Gordon field. The authors give one of the best explanations in the literature of why one must deal with the quantization of fields and not particles, the most important one being causality. Canoncial quantization is employed and the Feynman propagator for the Klein-Gordon field is derived. The Dirac field is also quantized using the canonical formalism. The authors show that Klein-Gordon fields obey Bose-Einstein statistics and Dirac fields obey Fermi-Dirac statistics. The all-important Wick's theorem is proven and higher-order Feynman diagrams are discussed. Most importantly, the authors show how to connect these results to experiment via the calculation of cross sections and decay rates. This entails the computation of the S-matrix elements from Feynman diagrams. The authors are very detailed in their elucication of the discussion, and those who have done these calculations know that it is great fun to do so. In addition, these "bread-and-butter" calculations give quantum field theory its ultimate justification in the modern particle accelerator. The discussion on radiative corrections is especially well-written, particularly the section on infrared divergences.
The authors do not entirely neglect the more formal aspects behind quantum field theory, and spend some time discussion renormalization and the amazing Ward-Takahashi identity. This important identity gives one further confidence in the consistency of QED in that is shows that timelike and longitudinal photons can be neglected in the actual calculations. The process of renormalization has been viewed with suspicion by mathematicians, but it has been given a firmer foundation recently using, interestingly, mostly 19th century mathematics. The authors discuss functional methods, and give an example of its use by calculating the photon propagotor. Viewing this as a constrained problem because of gauge invariance they use the Faddeev-Popov gauge fixing condition to obtain the correct results. In addition, they derive the important Schwinger-Dyson equations for QED using functional methods.
Effective field theories are also introduced in the book, with an explicit calculation of the effective action. The authors show the important connection between continuous symmetries and the existence of massless particles (Goldstone's theorem). Their discussion of the renormalization group is very understandable, and they motivate the subject well, by asking why the loop integrals over virtual-particle momenta are always dominated by values on the order of the finite external momenta.
Non-Abelian gauge theories are given a thorough treatment and Wilson loops are introduced as a comparator between gauge transformations at different spacetime points. The quantization of these theories is again done by viewing the quantization problem as a constrained problem, and the famous "Lagrange multlipiers", the Faddeev-Popov ghosts, are introduced. The authors show in detail how their introduction allows the correct Feynman rules to be produced, by showing that the unphysical timelike and longitudinal polarization states of the gauge bosons are cancelled by these fields. The BRST symmetry is discussed as a formal device to to this cancellation. The omit though how the Ward identities are derived from BRST symmetry.
The authors give the best explanation in the literature of asymptotic freedom by showing the effect of vacuum fluctuations on the Coulomb field of a SU(2) gauge theory.
The important operator product expansion is treated in the context of the Callan-Symanzik equation in quantum chromodynamics. It is applied to the deep inelastic scattering and electron-positron annihilation. Dispersion relations make their appearance here.
The authors also discuss anomalies and motivate the subject by analyzing the axial current in two-dimensional massless QED. The axial current is shown not to be conserved in the presence of an electromagnetic field, and they conclude that gauge invariance and conservation of axial currents in this theory cannot both be simultaneously satisfied. This is generalized to axial currents in four dimensions and the authors derive the famous Adler-Bell-Jackiw anomalies. The implications of anomalies for gauge theories are discussed along with observable consequencies.
The (mysterious) Higgs mechanism is also discussed and compared to the situation in superconductivity. To view it in terms of superconductivity I think gives it the most plausible and intuitive justification. Understanding the Higgs mechanism is a usual stumbling-block for newcomers to gauge theories, and the authors do a fair job here. The quantization of spontaneously broken gauge theories is then carried out, with emphasis on the Goldstone boson equivalence theorem. A brief discussion of the future of quantum field theory ends the book.
When reading this book, and others on quantum field theory, I am always amazed at the degree to which it works, and its elegance, despite the fact that it really is a collection of ad hoc strategies and sophisticated guesswork. One gets the impression that there is something profound behind the scenes, still waiting to be discovered, and which will be able to shed light on the major unsolved problem of quantum field theory: the existence of a bound state.
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on June 30, 2004
I used P&S for an intro QFT course. I learned much from the text as I found it clear and full of helpful examples. Particularly nice sections were those introducing free quantum fields, functional methods (path integrals), and non-abelian gauge theories and their quantization. In other sections, however, P&S often take many pages and indirect paths towards deriving basic results, which is particularly frustrating when one wishes to use the text for reference. The chapter introducing interacting fields seems disorganized, and the treatments of infrared and uv divergences (renormalization) seem to go on forever, with interesting or important results scattered through hundreds of pages. The discussion of the Standard Model is likewise overly verbose yet incomplete, and there is no discussion of susy. In this and other ways this text is less advanced than Ryder's, though I found its presentations clearer than Ryder's.
Overall, I found this a nice book to learn from, but horrible to return to when I try to fill in the gaps of my understanding of QFT.
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on December 7, 2005
If you are a thinker and want to deeply understand QFT, this book won't take you there. It provides nothing more than a sketchy summary of QFT which you might find helpfull if you already know the stuff. The most basic conceptual level needed by beginners to learn is missing. Logical carefull explanation is substituted with just 'mentioning'. Due to that even trivial statements explained in other books may sound cryptic in Peskin & Schroeder. Instead of focusing on the main topics and explaining them carefully, the book tries to cover a plephora of material and of course at the end you get a sketch not a detailed logical picture.

People that like this book probably are phenomenologists that compute Feynmann diagrams all day long and at the end of day you ask them a simple conceptual question and they don't know. Yeah ladies and gentlemen, computing Feynman diagrams and reading Peskin & Schroeder is not the same as understanding QFT.

I just finished a quarter of QFT course based on that book. The problems at the end of each chapter are interesting and important - I would say middle level difficulty. The beginners level is again missing. I had to solve a few problems directly from the book and the amazing thing was that every time I patiently read the text several days without being able to solve them. That's how well Peskin & Schroeder 'prepare' the reader for their own problems. At the end I open a book for beginners that cares to explain and voila - I solve the problem. My homework solutions usually get above 95% score but I definitely felt that wasn't due to reading Peskin & Schroeder.

The treatment of C, P, T symmetries in that book is a total confussion and is missing the idea why we choose to define those transformations that way (answer: we define these transformations so that certain lagrangian desities remain invariant or equivalentinly, certain equations of motion remain covariant). This is just another example how the book 'mentions' things instead of giving you the simple logical idea behind the scene. I found my current understanding of C, P, T symmetries in W. Cottingham's "An introduction to the standard model of particle physics".

To wet your feet I recommend Aitchison & Hey "Gauge theories in particle physics". It's not a perfect book either but you will pick up much more from it than from Peskin & Schroeder. Srednicki's textbook which is written in logical and modularized way is way better than P&S in terms of gaining understanding of QFT. Also search internet, many professors that teach QFT (and actually understand it) have written their own explanations some of which are pretty logical and usefull - see the lectures of Sidney Coleman if you can snatch them from the Harvard websites.
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on August 22, 2002
It is always extremely difficult to review any QFT text. This is no exception. I believe that a text should be judged on whether or not it succeeds at what it attempts; in this respect, I think the book is excellent. As many other reviewers have pointed out, this is a book that gives one detailed knowledge on how to calculate S-matrix elemtents and cross-sections, etc. If one thoroughly understands what is presented in this book, one is well poised to start a fine career in practical particle calculations. The flip side of this is that it is simply impossible to cover somewhat more abstract topics as elegantly as some other, more advanced texts. On the other hand, this has its advantages, especially for those who have already been introduced to field theory. For me at least, this book forced me to think deeply about what QFT is all about and how the different results of the theory fit together, just to stay afloat. This in and of itself was far more beneficial to me than any text that spells out the author's opinions on these questions could have been, since everyone has a completely different view on what QFT is about, and reading what someone else thinks it is about does not help the student who is beginning to form his own opinions very much. Getting into the details of the book, I felt that the authors did an excellent, thought provoking job on Wilson's beautifully simple ideas on renormalization; most texts treat the renormalization group as an advanced, mysterious tool, partly because it is usually presented after the older renormalized perturbation theory approach, but here Wilson's ideas are given top priority, and strong emphasis is given on the general applicability of the renormalization group to ANY field theory, be it in condensed matter physics or particle physics.
Also, despite what other reviews have indicated, I find the derivation of the LSZ reduction formula perfectly clear. The way it is derived is in my mind completely natural, namely by convoluting the n+2 point Green's function (for 2->n scattering) with wave packets that are simulateneously well seperated and have distinct momenta. The fields decouple, forming true asymptotic states and in the end producing propagators with poles at the physical masses and residues =SQRT(Z). The remaining factor is just the S-matrix element. What could be simpler than that? Incidentally, although the proof of renormalizability for gauge theories is not explicilty given, who needs it in a first or second encounter with field theory? I feel that the vast majority of students in this field do not need a proof right away. I think that almost the same thing could be said for most of the other rigorous derivations which are skipped in this book.
Although the text does not cover nonperturbative methods in any significant depth, I feel that it would be inappropriate to do so in a text of this type; after all, not all students taking first or second semester QFT end up using these methods on a day to day basis. In summary, I think this book covers the right topics for the audience that it reaches, and covers them well, if not entirely rigorously.
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on April 15, 2008
even years later now i still really dont like this book.
there is a gap in 1st year grad courses and this book.
Among other things i specifically dont like:
1) there is a shallow discussion of lie algebras
2) The notation can leave a newcomer confused in a field where clarity is essential to pedagogy
3) field theory isnt just QED and the standard model
4) there is a lack of nonperturbative topics
5) lack of fancier math
6) quantization is done entirely wrong, as if [x,p]~i came from nowhere. which leads to a convoluted (albeit original) tour through quantizing a dirac field
7) often the diagram and value of it are just stated in clever time and space saving ways which is detrimental to pedagogy again...
...the list goes on

I prefer:
1) ryder was easy for me to read when i started
2) bertlmann "anomalies" which is a book about much more than that
3) makeenko
4) A. Zee's tour of QFT
5) for getting into nitty gritty i liked ho kim an pham's particles book.

there are a lot of other good choices. mandl n shaw, srednicki, lowell brown's book, pokorski's, the whole series by greiner...those are also better in my view.

i think people only use this book because peskin is well known. the book doesnt have much merit from my perspective.
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on October 5, 1999
The book of Peskin/Schroeder represents in my view a major stepforward since Bjorken/Drell. Not only do they cover everything in moredetails but their book also reflect the considerable advancement and refinement of quantum field theory. In any case, one should still start with Bjorken/Drell in order to get a good understanding before moving over to Peskin/Schroeder. This is not to say that Peskin/Schroeder is difficult to read, quite the contrary, but the physics embedded in the mathematics will be much easier to master. The problems are very well tied to each chapter and are also clearly written for a further and deeper understanding of the subjects. Also, Peskin/Schroeder cover quite a bit in quantum field theory and one will never have the feeling that something was left out. This also makes it an excellent reference book as well.
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on July 22, 2001
I used this book for a year long quantum field theory course at Berkeley and feel that I learned a respectable amount from it. However, as the other reviews state, the book spends alot of time elucidating the details of the calculations in field theory while sacrificing pedagogical aspects. The little bit on representations of the Lorentz group is hardly enough to be satisfying. When I first went through this I was really wondering where in the world spinors came from (go to Pokorski's field theory text for this). Nonetheless, QED is done in a satisfying way, showing all the important calculations whose results are used throughout the text in the QCD and electroweak sections. Many sections of the book are not self contained at all. I wanted to learn about anomalies early on and found that the anomalies chapter could only be read after a thorough reading of all the QCD chapter (which is particularly phenomenological). The renormalization chapters are quite good, but it lacks a big-picture summary of how to go from measurable quantities to things like running coupling constants.
P&S do a good job of writing a very phenomenologically oriented field theory text. There are practically as many connections to experiment as you would find in a decent particle physics book. The formal structure of quantum field theory is not explored at all. Chapter 7 holds many formal results which are important for the rest of the book, however the chapter is particularly confusing. Functional integrals are explained but are not taken as the foundation upon which the QFT stands. I found the formal structure of QFT to be very well explained in Pokorski's text. In the end, Peskin is a pretty good book with which to start learning QFT. I have yet to find an introductory QFT text that I really like (I haven't checked out the Brown book). Peskin left me feeling like I knew how to do particle physics calculations correctly but I didn't really get a feel for how QFT as a logical framework fit together. After reading Peskin, one is comfortable enough with calculating in QFT to a degree that more sophisticated texts (Pokorski, Weinberg) are very accessible.
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